Rotary pump



Dec. 13, 1949 A, zE|T| |N 2,491351 ROTARY PUMF Filed Sept. 18, 1944 IN VEN TOR.

manna Dec. 1a, 1949 UNITED STAT\ES PATENT' OFFICE ROTARY PUMP Alexander Zeltlin. New York, N. Y. Application September 18, 1944, Serial No. 554,600

` 4 onims. (ci. 108-188) This invention relates to rotary pumps or compressors of the sliding vane type. In these pumps, the rotor rotates about an axis within an eccentric bore and carries the sliding vanes which are at all times in engagement with the walls of the bore. The vanes are thus caused to oscillate toward and away from the rotor axis to form alternately increasing and decreasing chambers for receiving and discharging fluids.

The shape of the eccentrio bore will determine whether the pump will operate smoothly and withous vibration so as to avoid undue wear and to deliver substantially pulsationless flow. The problem of properly designing the bore to accomplish these functions is one which on its face appears deceptively simple; but the large number of solutions heretofore proposed, in patents and elsewhere, are proof of the inherent difilculty.

It has, for example, been proposed to employ two circular arcs, of different radii and diametrically oppositely positioned, joined by Archimedean spirals or by parabolas. there resulted points of junction between the spirals or parabolas and the circular portions, 'which formed kinks or cusps, and resulted in vibration, uneven operation and undue wear.

It is therefore one of the principal objects of my invention to design a bore for a rotary pump of the sliding vane type which will be free of the objections present in designs heretofore proposed. Such bore will have the following characteristics:

1. The points of junction between the non-circular parts of the bore and the circular parts will be smooth, i. e., free of kinks or cusps.

2. The non-circular parts of the bore will be a curve which will provide smooth, steady, substantially pulsationless flow.

3. The diameter of the bore through the center of rotation will always remain constant to provide a constant degree of clearance between the vanes and the bore.

4. The design of the non-circular parts of the bore is such that they can cooperate with circular parts of varying angular length.

Further objects and advantages of this invention will become apparent in the following detailed description thereof.

In the accompanying drawings,

Fig. 1 is a cross-section through a rotary pump of the sliding vane type.

Fig.,2 is a diagrammatic development of an Archimedean spiral type of eccentric bore heretofore used and demonstrating the problem.

In all of these instancesv Fig. 3 is a view similar to Fig. 2 showing the development of the type of bore employed herein.

Fig. 4 is a diagrammatic representation of a bore embodying the prinoiples of this invention.

Referring to Fig. 1 of the drawings, there is shown the body Ill of a rotary pump casing having a bore l which is formed of two diametrically-opposed circular sections 12 and |3 of different radii from a common center 0 and' connected by curves ll, ll' of special design to be more fully described hereinafter. The rotor 20 is mounted for rotation about axisO and is of substantially the same radius as circular section |2 against which it bears. The rotor is provided with transverse,vdiametric slots 22 within which operate vanes 23 of a length equal to the sum of the radii of circular sections`|2 and |3. The vanes may be provided with bearing elements in the form of rockers 25 at their outer ends b'earing on the inner surface of the cylinder bore. It will be understood in the following description that references to the length of vane includes the radial projection of the rockers, and it will be further understood that the necessary clearances are implied. Also, the terms "pump" and "compressor" are used interchangeably. The vanes are provided with intermediate cut-out portions 26, 21 to enable them to clear each other. Inlet and outletports 28 and 29 are provided.

Except for Vthe special design of connecting curves ll, H', the above description covers the familiar elements of the rotary vane-type pump or compressor. It is apparent that as the rotor rotates, the ends of the vanes at one side are forced into the rotor while those at the other side are forced out of the rotor. The latter form with the cylinder bore an expanding chamber for drawing fluid into the pump, while the former constitute the discharge or pressure side by reason of a continuously decreasing chamber. In the case of an incompressible fluid, such as a liquid, the inlet and'outlet ports are co-extensive with the connecting curves H, H', but in the case of compressible fluids, such as air or gas, the inlet and outlet ports may be of lesser length than the connecting curves.

We come now to the design. of the connecting curves ll, Il'. The desirable conditions 'which should be present have been set forth in the introduction hereto. By referring to Fig. 4 it will be seen that the position where the vane is symmetrically positioned with respect to the rotor, i. e., where the vane projects equally at` each side, is indicated at D-O-D'. In this position the radius vector OD is equal to the radius vector OD is equal to radius vector OD'.

- line DOD'.

A al'CS.

between the vane length and the rotor dlameter..

as a power series. or logarithmlc, exponential orA trigonometric equation. Each of lthese equations will have in common the characteristic that they employ a number of terms, each term including a coefiicient, corresponding'rto the Vnumber of conditions to be satisiied.l Thus, for example, the curve may be expressed in the conventional manner of a power series:

This difference is indicated as p. At points D and D' the vane projection is, therefore, p/2, and this' is the only position where radius vector If the varlation of the radius vector of curve |4 or ll' at any point from the value 0D or 0D' is indicated by the variable r, it is apparent that i r=a function of a, or r=F(a) (1) where a is measured from the symmetrical base r=0, or F(ao) =0. At point A (where the con- Thus, for a=ao=0, .i. e., at point D,

necting curve joins the circular curve) =m and It has long been known that the smoothness of operation'of this type pump depended upon how smoothly the connecting curves |4,.|4' could be joined to the circular arcs |2 and |3. As pointed out hereinbefore, Archimedean spirals and parabolic curves were found not to be the complete solution of this problem. Thus, Fig. 2 illustrates the development of a cylinder bore employing an Archimedean spiral to join the circular The kinks are plainly visible at the points of junction A and B. Since at the point of junc-` v tion A there is zero vane projection, i. e.,

and therefore it has been proposedi to devise a curve wherein the first derivativeof F(z)=0. This was found to be insufiicient, -and I have determined the cause as residing in the factthat it is necessary for the connecting lcurve to be such that not only the first derivative, i. e., the change of value r with respect to angle a is zero at point A, but also the second derivative, i. e., the rate of change of r with respect to angle zz must be zero at point A in order to obtain a curve as illustrated in Fig. 3 in developed form, which not only has no kinks at the points of junction with the circular arcs, but also results in the maximum of smoothness of junction. I have, then, these conditions which my connecting curves must fulfill:

where F' indicates the first derivative of r with respect to a and F indicates the second derivatve.

A curve, F(a) embodying these conditions may be satisfied by various equations for a curve, such By setting up four equations corresponding to the four conditions to be satisfied, the values of the coeflicients A, B, D and F can be determined. These four equations are:

We solve these equations for the values A, B, and F, and obtain the following:

u Qui 5 1 8 1 A-' 3-16 P a; D- p'' F-rs'PTf |1Vhe equation of the connecting curve which Satisfies the four conditions thus becomes:

The value of al depends upon the length of the circular arc', and this length as well as the value of p are determined by considerations of design.

T o illustrate the general principles involvedei'n selecting an equation which will satisfy the four fundamental conditions, still another example is here given, this time in the form of a conventional exponential equation for 'a curve:

Here, too, in order to determine the values of. the coefiicients A, B, C and D, for equations are set up in Equation 12 embodying the conditions of Equations 2, 3,4 and 5:

From these four equations the values of A, B. C and D can be determined. Here, also, the equation will be defined in terms of p and m1, for by solving the above equations there is obtained the following values for the coeflicients:

These examples of equations for the connecting curve which will satisfy the conditions set forth herein are suificient to illustrate the 'general method of obtaining such equation.: The equation must at least as many terms as there are conditions to be satisfied, each term including a coemcient, whereby the coeflicients may be determined by setting up a plurality of equations each corresponding to one of the conditions., It will be understood that if more than four conditions must be satisfied. each of the Equations 6 and 12 cited above will have additional terms. Thus, if a fifth condition is added to those set forth in 2, 3, 4 and 5, the power series 6 will be extended as follows:

Second, the equations which will satisfy the curve, whether said equations are a power series, exponential, trigonometric or logarithmic equation, are all characterized by the fact that both the flrst and second differentials at point A (ai) ar zero. Third, in any of these equations the second. diiferential is not a constant but is expressed in terms of variables (p and m1) so that by selecting. proper values of these variables the second differential may be made zero. This would be impossible in any case where the second diflerential was a constant, as, for instance, in the case of a parabolic spiral which takes the form r=a02+c and yields a second derivative v v aga-21,1 v

'I'hus by setting forth the conditions which govern the design of the connecting curve, an equation which satisfies thecurve can readily be obtained. These conditions insure a junction of. the connecting curve with the circular arc which' is not only without kinks or cusps, but which is smooth. Such a bore will yield maximum smooth'- ness in operation, substantially pulsationless flow; and a minimum of vibration and wear.

In accordance with the provisions of the patent statutes, I have hereindescribed the principles and operation of my invention, together Awith the apparatus which I now consider to represent the best embodiment thereof, but I desire to have it understood that the apparatus shown is only illustrative and that the invention can be carried out by other equivalent means. Also, while it is designed to use the various features and elements in the combination and relations devF' represents the flrst diflerential of r with respect to ai, where r is the diiference in length between the radius vector at the base-line and the radius vector to any other point of the bore F" represents the second difierential of r with respectto a.

2. In a rotary pump or compressor having a body provided with a cylindrical rotor. said body having a bore eccentric-with respect to the rotor, said bore comprising two diametrically opposite circular arcs of unequal radii joined by noncircular connecting curves, said rotor and said circular arcs having a common center, the radius of the rotor being substantially equal to the radius of the ysmaller arc, said rotor having radial slots, and vanes slidable in said slots, the length of said vanes being substantially equal to the sum of the radii of the two circular arcs, said vanes being adapted to be in contact with the bore in all positions. and said connecting curves being' adapted to extend and retract the vanes. characterized by the connecting curves being so formed that'they can be expressed in the form scribed, some of these may be altered and others omitted without interfering with the more gen'/` eral results outlined, and the invention extends to such use. r

Having described my invention, what I lclaim and desire to secureby Letters Patent is:

1. In a rotary pump or compressor having a body provided with a cylindrical rotor, said body having a bore eccentric with respect to the rotor, said bore'comprising two diametrically opposite circular arcs of unequal radii joined by non-circular connecting curves, said rotor and said circular a'rcs having a common center, the radius of the rotor being substantially equal to the radius of the smaller arc, said rotor having radial slots, and vanes slidable in said slots, the length of said vanes being substantially equal to the sum of the radii of the two circular arcs, said vanes being adapted to be in contact with the bore in all positions, and said connecting curves being adapted to extend and retract the vanes, characterized by the connecting curves being so formed that they can be expressed in the form of a basic equation for F (a) in which F' (a1)=0 and F (a1)=0, wherein F represents function of a represents the angle between a base-line where the vanes project equally at opposite sides of the rotor and a radius vector drawn from the axis of rotation to a point on the bore of a basic equation for F(u) in which F'(a1) =0, and F'f'(a1)=0, and in which F"(a1) is a variable whereby it may be made equal to zero at selected values of a, wherein arc F' represents the first differential of r with respect to a, where r is the difference in length between the radius vector at the base-line and ghe radius vector to any other point of the ore F"represents the second diflerential of r with respect to a.

3. In a rotary pump or compressor having a body provided with a cylindrical rotor, said body having a bore eccentric with respect to the rotor, said lbore comprising two diametrically opposite circular arcs of unequal radii joined by noncircular connecting curves, said rotor and said circular arcs having a common center, the radius of the -rotor being substantially equal to the radius of the smaller arc, said rotor having radial slots, and vanes slidable in said slotsI the length of said vanes being substantially equal to the sum of the radii of the two circular arcs, said vanes being adapted to be in contact with the bore in all positions. and said connecting curves being adapted to extend and .retract the vanes, characterized by the connecting curves being so formed that they can be expressed in the form of a basic equation for F(a)` consisting of as many terms as there are conditions to be fulfllled, each term including a coeflicient, said conditions being Finn) =0,

F'(ai) =0. and 1""(a1)=0, the coeflioients being determined by setting up a plurality of equations formed by embodying each of said conditions successively in the basic equation, wherein F represents function of" .z represents the angle between a base-line where the vanes project equally at opposite sides of the rotor and a radius vector drawn from the axis of rotation to a point on the bore zm represents zero value of a zu represents the angle between the base-line and the radius vector to the point of junction between theconnecting curve and the circular arc F' represents the first differential of 1' with respect to a, where r is the difference in length between the radius vector at the 'base-line and the radius vector to any other point of the bore F represents the second diiferential of r with respect to i p represents the amount by which the length of a vane exceeds the diameter of the rotor.

4. In a rotary pump or compressor having a body provided with a cylindrical rotor, said body having a bore eccentric with respect to the rotor. said bore comprising two diametrically opposite circular arcs of unequal radii joined by noncircular connecting curves, said rotor and said circular arcs having a common center, the radius of the rotor being substantially equal to the radius of the smaller arc, said rotor having radia] slots, and vanes slidable in said s1ots,,the length of said vanes being substantially equal to the sum of the radii of the two circular ares, said vanes being adapted to be in contact with the bore in all positions, and said connecting curves being adapted to extend and retract the vanes, characterized by the connecting curves being so formed that theycan be expressed in the form of a basic equation for F(z) consisting of as many terms as there are conditions to be fulfilled, each term including a coefiicient, said conditions being F010) =0,

formed by embodying each of said conditionssuc-l cessively in the basic equation, F"(a1) being a variable whereby it may be made equal to zero at selected values of zz, and wherein F represents function of represents the angle between a base line where the vanes project equally at opposite sides of the rotor and a radius vector drawn from the axis of rotation to a point on thebore ao represents zero value of a ai represents the angle between the base-line and the radius vector to the point of .function between the connecting curve and the circular arc F' represents the first difierential of r with respect to a, where r is the difierence in length between the radius vector at the base-line and the radius vector to any other point of the bore F" represents the second differential of r with respect to a p represents the amount by which the length of a vane exceeds the diameter of the rotor.

ALEXANDER ZEITIJN'.

REFEREN CES CITED UNITED S'I'ATES PATENTS Name Date Curtis July 11, 1939 FOREIGN PATENTS Country Date Great Britain Nov. 8, 1923 Number Number 

